The starter on my 1991 mustang sporatically stays engaged and running even if I turn off the ignition. I've replaced the starter, battery and solinoid. I have to disconnect the battery to stop it.

-the wires are not correctly re-installed for the starter.
- u may need wiring diagram
Did you take pictures before you took it apart, or did you tag wires before unconnecting them.

IT sounds to me like the solenoid is sticking. Follow the large wire up from where it bolts onto stater and the next thing that wire is bolted to is the solenoid.

To check if it is the ignition switch remove the small wire from the starter and place a multimeter on the wire to earth you will have 12v dc when you put the switch in the start position IF this is so remove the starter as it will be either the starter solenoid or a s/ motor fault

Find the starter solenoid near the battery. When the starter sticks on remove the small wire from the starter solenoid. If the starter stops the issue is in the ignition switch side of the circuit. If the starter continues to run with the small wire removed you have a bad solenoid. You can also try tapping the solenoid with the handle end of a screwdriver. If the starter stops when you tap it, replace it. Let me know if you have any questions and I'll do my best to answer them. Thank you for using FixYa.com!

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

Hello, There are small wires that attach to the Starter Relay. These are the wires Mechanics call "tickler" wires. There should not be power going through the tickler wire unless the Ignition switch is turned to the START position.

Disconnect the small wire off of the Starter Relay. Leave it off and put your battery cable on the Battery. The Starter should not crank. The Ignition should be OFF.

Now we need to find out where the tickler wire is getting power from. Put a Multimeter or test light on the Tickler wire for POS and ground the other wire on the tester to a NEG ground. I suspect your problem is in the Interlock switch. The Interlock switch would be on the Clutch pedal lever under the dash for a standard shift.

If you had an Automatic transmission, the Interlock would be in the shift linkage or Brake pedal lever. Without changing from an Auto to a Standard trans people have trouble hitting the under dash Interlock switch with their shoes getting in and out of their cars. Even while driving you can hit the under-dash switches with your shoes.

So check under the dash for a broken or dislocated switch on the Clutch or Brake pedal levers. Then move the switches until the Test equipment shows the power is not going to the Tickler
wire . Once you do this you have to make the START position work on the Ignition switch. Leave the tickler hooked up to the test equipment until you get the wiring right. You may have to adjust the Ignition shift-rod in the steering column so that START means the correct thing only in the start position.

I hope my solution is very helpful in giving you ideas about fixing your car.

solenoid may be sticking. Have someone start the car, if it sticks tap the solenoid with screw driver handle. If that stops the starter, replace the solenoid. If it were me, I wouldn't bother testing it and just replace solenoid.

could be an intermittant open in the starter With and assistant wile you are trying to start it. hsve the asst smack the starter with a hammer. If it starts , REPLACE THE STARTER. Hope this helps

what happens if you pull the shift lever into gear to cut off the neutral-park safety switch? This cuts pwer from the key to the starter solenoid. If that fixes it, replace the igniton switch.

which solenoid did u replace? the one on the starter or the main on up top near the battery, those are the ones that stick closed and keep the starter engaged. here is a picture.

Bad ignition switch or starter seleniod